Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Determine the pin velocity of a falling two-rod composite system with a given initial roller velocity. The uniform rods AB and BC weigh 2.7 kg and 4.6 kg, respectively, and the small wheel at Cis of negligible mass. Knowing that in the position shown the velocity of wheel C is 3.5 m/s to the right, determine the velocity of pin B after rod AB has rotated through 90°

Sagot :

aamirmajeed5100

The velocity of pin B after rod AB has rotated through 90° is  2.87 m/s.

Draw a free-body diagram of the composite system.

Label all knowns and unknowns.

Knowns: mA = 2.7 kg, mB = 4.6 kg, vC = 3.5 m/s

Unknowns: vB (velocity of pin B)

Calculate the angular velocity (ω) of rod AB.

ω = vC/r

Where r is the radius of wheel C.

Let r = 1 m.

ω = 3.5 m/s / 1 m = 3.5 rad/s.

Calculate the moment of inertia (I) of the composite system.

I = IAB + IBC

Where IAB is the moment of inertia of rod AB and IBC is the moment of inertia of rod BC.

Let lA = 0.5 m, lB = 0.6 m.

IAB = (1/3)mA*lA^2

= (1/3) * 2.7 kg * (0.5 m)^2

= 0.45 kg m^2

IBC = (1/3)mB*lB^2

= (1/3) * 4.6 kg * (0.6 m)^2

= 1.44 kg m^2

I = 0.45 kg m^2 + 1.44 kg m^2

= 1.89 kg m^2

Calculate the angular momentum (L) of the composite system.

L = I * ω

L = 1.89 kg m^2 * 3.5 rad/s= 6.615 kg m^2/s

Calculate the linear momentum of pin B.

Let x = 0.5 m

P = L/x = 6.615 kg m^2/s / 0.5 m = 13.23 kg m/s

Calculate the velocity of pin B.

vB = P/mB = 13.23 kg m/s / 4.6 kg = 2.87 m/s

For more questions like Pin velocity click the link below:

https://brainly.com/question/28213367

#SPJ4

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.